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There are even banks that offer to change these numbers at will.These numbers are therefore impossible to compute without knowing the algorithm and the key, and there is no relation to Luhn's algorithm.
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As a followup to my recent post about what your credit card number means, I wanted to throw out a bit more credit card trivia and talk about how you can tell if a credit card number is valid.
As you may or may not aware, most credit card numbers are generated based on something known as the Luhn algorithm.